The letter, written by Mrs May's private secretary, says she believes the plan is "unacceptable".

On Tuesday, Mr Hunt set out a strategy to give UK tourism a boost following London's Games and said ministers were looking at simplifying visa applications for non-EU nationals.

'Chinese criminals'

The strategy focused on attracting visitors from China, where the government thinks there is potential to triple the number of tourists - generating more than £500m in extra spending and creating more than 14,000 jobs.

In the absence of concrete data about visa abuse, it is impossible to determine whether the right balance is being struck between the UK's commercial interests and its security needsMark Tanzer, Association of British Travel Agents

Currently, visitors can apply for a single visa to visit much of Europe - but a separate one is required to travel to the UK.

Countries such as France and Germany are far more successful at attracting Chinese visitors, and the UK could do better if getting a visa was easier, Mr Hunt has suggested.

But a letter from Mrs May's private secretary to the prime minister's private secretary said the current rules were a "key tool in protecting the public against significant harm".

There are already 400 Chinese criminals awaiting deportation and 1,000 asylum applications from Chinese citizens last year, it said.

"The proposal... is not acceptable to the home secretary for national security reasons," the letter said.

But Mark Tanzer, chief executive of the Association of British Travel Agents (Abta), said: "In the absence of concrete data about visa abuse, it is impossible to determine whether the right balance is being struck between the UK's commercial interests and its security needs."

He argued that "proper visa monitoring and reporting processes" were needed, and any abuses of the system could be addressed as they arose.

"We must not forget that visas are only one of the factors that deter Chinese tourists from visiting us - lack of air routes and high aviation taxes also depress demand," he added.

Mr Tanzer has previously said his organisation "welcomed" Mr Hunt's position as "a step in the right direction".

Nobel prize winners

Meanwhile, Immigration Minister Damian Green told that a visa scheme had failed to attract as many of the most talented artists, musicians and scientists to come and work in the UK as the government had hoped.

"We offer a thousand visas a year for the exceptionally talented," Mr Green said.

"In its first year in operation it came nowhere near using them all.

"That tells me we need to fine tune the system to make sure that around the world, if you are a bright young artist or a gifted young scientist, you know there is this route to come and work in Britain. We need to do better on that."

The minister added: "If you are a current Nobel Prize winner, you won't find it very difficult to get into this country.

"But we want the next generation of Nobel Prize winners, so we have carved out a specific route in the immigration system."